Research interest

[student research topic]

• One  research topic related to "the Zero-Range Process". The toy model simulates 'grouping' behavior of animals, snow particles, insects, etc. In 1D geometry, entities constituting a system may be condensed (grouped) to a single location, then the group disperses after some time then condensed to another location. It shows meta-stable grouping motion by mutual interaction among entities, and it shows phase transition in out-of-equlibrium condition. The project is to study the behavior numerically and then analytically. 

• Students who took one year thermodynamics and statistical physics are qualified. The project will be mainly conducted in winter/summer break. Stipend will be provided. The position is for one student. Contact me for your inquiry and application. 

Continuous flocking transitions in active matter (led by Dr. Wanming Qi)

• Active matter systems such as bird flocks, insect swarms and cell sheets are driven out of equilibrium by energy injection at the single-particle level. It is of fundamental interest to understand the emergent collective behavior of such interacting non-equilibrium systems. One of the simplest, but fascinating, phenomenon is flocking, where many self-propelled individuals interacting via short-range alignment interactions self-organize into collective motion.

• Natural flocks and swarms are found to exhibit critical behaviors associated with continuous random-to-flocking transitions at finite-size. Dr. Qi is interested in investigating the finite-size scaling properties at such transitions to help understand what physics governs the observed scaling behaviors of real animal groups. The ideal case of incompressible systems in 2D was worked out through a combination of numerical simulation and theory [arXiv: 2211.12025 (2022)]. On-going work is about extending the study to the more realistic weakly compressible but homogeneous case and to 3D.

Quantum capacitance of nanoelectromechanical devices

• The concept of capacitance is familiar to us as an electric circuit element. It measures the amount of charge induced by the unit voltage change.  In a metal, electrons are occupied according to the Fermi-Dirac distribution up to the Fermi level. The extra charges induced by an external voltage source will shift the Fermi level (because no two electrons can occupy the same state, Pauli). The shift is inversely proportional to the electronic density of states in the metal, and the ratio of induced charge and the shift of the Fermi level is the quantum capacitance. 

• A nanometer size electro-mechanical system provides interesting opportunity where the role of quantum capacitance becomes noticeable due to its small (surface area, therefore) classical capacitance. Massless Dirac material (dos~0) is one extreme, and the flat band (dos~infty) is the other extreme. 

The Anderson transition in chiral symmetric quantum matter 

• 1-dimensional chiral symmetric wire with random hopping strength shows the phase transition at energy zero. In the thermodynamic limit, nonzero energy states are spatially localized, while at zero energy the density of states diverges logarithmically, which pauses a possibility to avoid the Anderson localization. 

• Within the localization length, which diverges as energy approaches to zero, the system is self-similar and correlation functions decay algebraically. The computation of critical exponents that characterize the algebraic decay and the inverse participation ratio was worked out. [Ref: PRB 56, 12970, 1997] in theory, but has not been observed in experiment. I am interested in proposing an experimental setup to measure them in more generalized chiral symmetric systems. 

Thermodynamic uncertainty relation

• How much work can we get out of a thermal machine by transferring heat Q? Recall the Carnot, Otto, and Stirling engines that you learned in freshmen physics courses. The extraction of work comes at no production of entropy for an adiabatically proceeded thermal cycle. Only in ideal (thus, unreal) condition, the thermal efficiencies in textbooks are achieved. Dealing with thermal reservoirs, we can't avoid talking about thermal fluctuation, which generates noise in particle and heat transport. 

• The message of the TUR is the following: only we are able to increase the precision of current measurement at the expense of entropy production. The multiplication of the two is lower bounded by the Boltzmann constant. I am much interested in the validity of the statement in quantum systems driven by multiple frequencies.

Quantum walks in synthetic space

• A classical Brownian motion modeled by the random walk is due the thermal fluctuation of an environment in which an object (say, pollen) is subjected.  Simplifying its motion, each time step the object has a choice to walk left or right with equal probability. Its diffusion in spacetime is thus associated with the thermal fluctuation represented by temperature (the fluctuation-dissipation theorem). 

• The quantum walk of an wavefunction is governed by a discrete unitary time evolution operator. Interestingly, the operator can be prepared in a time dependent manner to let it explore synthetic dimensions in addition to the real space dimension the wavefunction is located. Can you also walk synthetic? 

• A time evolution of quantum mechanical states by a time periodic Hamiltonian may contain extra information of topology in the time domain. As a result, there are examples of topological Floquet matter that are distinct from static counterparts. I would like to introduce a time evolution operator that simulates the low energy physics of topological metal. The evolution comes with strong disorder mixing information in the quasi-energy domain. I provide concrete numerical evidences testing the topological metallicity and simple experimental proposals identifying them.